Supergravity, M theory and Cosmology

TL;DR

This paper surveys attempts to reconcile cosmology with supergravity and M/string theory. It identifies a universal mass-quantization relation in extended supergravities with de Sitter vacua, predicting ultralight scalars of order $m \sim H$ and exploring implications for cosmology. It then presents D-brane constructions that reproduce hybrid inflation dynamics (P-term inflation) and analyzes several brane realizations (D4/D6, D3/D7) with Fayet-Iliopoulos terms driving, stabilizing moduli, and concluding in SUSY vacua. Finally, it extends to M-theory compactifications on four-folds with G-fluxes to realize a cosmological evolution with Coulomb and Higgs phases, anomaly cancellation, and a noncommutative instanton interpretation. The work highlights how these string/M-theory structures can inform early- and late-time cosmology and outlines remaining open questions.

Abstract

We discuss some recent attempts to reconcile cosmology with supergravity and M/string theory. First of all, we point out that in extended supergravities the scalar masses are quantized in terms of the cosmological constant in de Sitter vacua: the eigenvalues of the Casimir operator 3 m^2/Λtake integer values. For the current value of the cosmological constant extended supergravities predict ultra light scalars with the mass of the order of Hubble constant, 10^{-33} eV. This may have interesting consequences for cosmology. Turning our attention to cosmological implications of M/string theory, we present a possibility to use string theory D-brane constructions to reproduce the main features of hybrid inflation. We stress an important role played by Fayet-Iliopoulos terms responsible for the positive contribution to the potentials and stabilization of moduli.

Figures (7)

• Figure 1: Cosmological potential with Fayet-Iliopoulos term; notice the dS valley is classically flat; it is lifted by a one-loop correction, corresponding to the one-loop potential between branes. In this figure the valley is along the $|\Phi_3|$ axis; the orthogonal direction is a line passing through the origin of the complex $\Phi_2$ plane and we have put $|\Phi_1|=0$. Notice there is no $\bf{Z}_2$ symmetry of the ground state, it is just a cross section of the full $U(1)$ symmetry corresponding to the phase of the complex $\Phi_2$ field.
• Figure 2: Cosmological potential without Fayet-Iliopoulos term.
• Figure 3: Brane configuration evolution. a) For $\phi\neq 0$, supersymmetry is broken and D4-D6 experience an attractive force. b) At the bifurcation point, a complex scalar in the hypermultiplet becomes massless; when we overshoot tachyon instability forms, taking the system to a zero energy ground state shown in c) .
• Figure 4: The D3/D7 "cosmological" system. The 3-3 strings give rise to the ${\mathcal{N}}=2$ vector multiplet, the 7-3 strings to the hypermultiplet and the worldvolume gauge field ${\mathcal{F}}$ to the FI terms of the $D=4$ gauge theory.
• Figure 5: The "snowman" fibration of the $K3\times K3$ four-fold. The crosses indicate points on the ${\mathbb C}P^1$ basis at which the fibre tori degenerate. In the orbifold limit of the 'top' K3 there will be four such points.